In the centre of every cell of a 5x5 board stands one kangaroo. Suddenly, a thunder strikes,
and each kangaroo is startled so that it jumps over the side of its cell into a neighbouring cell,
possibly joining one or more other kangaroos there. What is the greatest possible number of
cells that are now empty?
The answer is 16, but it is tough for me to get to that answer.
if they all jump toward the center, the entire outer row of cells is empty (16 cells)
Im starting to think they made a mistake in the question. I really think the right answer is 15
Hm, scott, hold on a minute. Can they jump diagonally? This is an 8th grade test problem, so I'm assuming yes?
they cant jump diagonaly
okay ... no "corner" (diagonal) jumping
in the outer row (5 x 5); cells adjacent to the corners, jump to the corners
... cells in the middle of a row, jump toward the center
... 12 cells empty
in the next inner row (3 x 3); corner cells jump to the middle of their row/column
... 4 more cells empty
the center cell jumps to the adjacent row/column cell
... for a total of 17 empty cells
16 does not appear to be correct
oops ... 16 is correct
everyone HAS TO jump
the cells in the middle of the 3x3 rows jump to the center cell ... which does not stay empty